How does a matrix diffraction grating affect radius/intensity of the dots?

Here's a question I have so far not been able to find an answer to:

How does a N x N dot-matrix diffraction grating affect the radius and intensity of the individual dots relative to the beam of the laser diode? Which characteristics of grating and laser module are relevant factors?

What I want to achieve is to project a matrix of laser dots, each roughly equivalent in intensity to a 5mW green laser pointer, to keep it eye-save. To do this, I have to somehow determine the required power of the laser module.

Any information would be very much appreciated!

/Gerald

As the Laser's Beam goes through the dual axis Diffraction Grating
each dot from the central dot will get weaker...


BTW...

to the Forum...
Don't forget to read the Newcommers section aqnd trhe Forum Rules...


Jerry

Thanks for the quick reply, lasersbee!

So the intensity of the projected dots is NOT uniform, but diminishes with incresing #order. Is that what you were saying?

I could live with that as long as all dots are bright enough as well as eye-save. What I'm looking for, is a more formal description of the relation between the projected dots and the source beam.

The question to which I ultimately want to find the answer is: What power should the laser module have, so that each dot, projected through a NxN diffraction grating (e.g. N=16), has roughly the brightness of a green 5mW laser pointer (projected from the same distance)?

I'm sorry to give you a delusion, but isn't this way that it work ..... the "main" beam (axial with the input one) is the more strong, then, time by time it get diffracted, it become weak, so the first diffraction is weak, the second is weaker, the third also more, and so on ..... going away from the axis of the original beam, each other one, more is far, more is weak ..... so, is practically impossible have a grid of dots that have the same apparent intensity .....

Thanks HIMNL9! I'm aware that the intensity of the interference peaks will decrease with every #order. But there has to be a way to quantify the intensity range from #0 to #N so that it becomes possible to estimate the power required for the source. I would rather like to do this on paper than having to do trials with various laser modules and a power meter.

You are basically asking members of the Forum to invest their time to do
these test for you...
I think the easiest way is to get a Double Axis Diffraction grating and do
the tests yourself... Or you can do a Google search for some formula...

Here is an example of Double Axis Diffraction Grating we have in the Shop...

Diffraction Grating Slides - Double Axis 13,500 line/in


Jerry

No, that is not my intention at all. I just thought that there might be existing knowledge I could use - if not formalized, then at least empirical. And of course am I always doing extensive google searches before bothering anybody on a user board. The problem is, that this is a fairly specific scenario from a scientific point of view, compared to a practical point of view: I'm surely not the first person to want to know how bright the diffraction pattern will be, before actually buying the components.

So if anybody here has more information on this topic or can point me to other resources, then that would be fantastic.

Perhaps you could get a hold of a Diffraction Grating manufacturer...
they may have additional info on your question...
We personally have never needed to know the power of every Laser
dot through a diffraction grating... so we have never tested it....


Jerry

I don't think any optic has 100% efficiency in diffraction... Your best bet would be to get as many 5mW lasers as you want 5mW dots...

I dont have the math in my head, but i'm sure it should be possible to calculate the relative intensities of all the dots relative to the beam that goes straight through.

There arent that many factors involved: just wavelength/lines/mm and the dark-transparant ratio of the grating, or am i missing some other relevant factor?

Yes, that's what my intuition tells me too. But I think the radius of the source beam would also be a factor.

The problem is, all I could find after a couple of hours of research, is the Fraunhöfer diffraction formula (http://en.wikipedia.org/wiki/Fraunhofer_diffraction), which can be used to calculate intensity and spread of the interference pattern of a 1D-single-slit scenario. But I have absolutely no idea how this already very complicated piece of mathematics could be translated to suit a 2D-multi-slit scenario, i.e. diffraction grating.

i have 12"x8" sheets of dual axis diffraction grating and in my observance... distance from laser to sheet affects out put. Also, what is see is from the out puts center on the wall the "dots" get weaker uniformly the further out the "dot" pattern gets.

onspey said:

Yes, that's what my intuition tells me too. But I think the radius of the source beam would also be a factor.

The problem is, all I could find after a couple of hours of research, is the Fraunhöfer diffraction formula (Fraunhofer diffraction - Wikipedia, the free encyclopedia), which can be used to calculate intensity and spread of the interference pattern of a 1D-single-slit scenario. But I have absolutely no idea how this already very complicated piece of mathematics could be translated to suit a 2D-multi-slit scenario, i.e. diffraction grating.

Click to expand...

I happen to be getting my PhD in something related to diffraction, specifically, manufacturing complex grating structures, and I can tell you that quantifying scientifically the intensity of the diffracted beams is very hard to obtain even for 2D gratings. There is software out there but it is really expensive and my boss won't even purchase that.

What I can tell you though, from personal experience fabricating 1D and 2D gratings is that the 2D gratings behave in the same way as 1D gratings but with powers reduced, in terms of the orders, it is correct to assume that the intensity drops as the order # goes up. Yes, the main beam will have most of the power, but that depends on how efficient the grating is. Grating efficiency is very hard to understand and model, especially for 2D gratings and complex structures the equations are just too mathematically complex to even bother solving. The efficiency of the gratings depends on several factors, like wavelength, shape of the grooves, depth of the grooves, etc.

To clarify something, any sort of periodic array of elements is itself a diffraction grating, even a 1D set of lines. The number and type of periodicity translates into the shape of the Fraunhofer diffraction pattern; for example a set of parallel lines gives a set of dots in a line. Lines in two dimensions (or any sort of arrangement with 2 periodicities) gives a diffraction pattern with 2 periodicities as well, usually an arrangement of dots in a square like fashion, much like you are describing.

Getting an equation specific for an NxN matrix is something I haven't looked up, but there are articles like this one that have information on this.

My best recommendation would be to just measure the power of the reflected beam, which should be the highest, and adjust your power accordingly so it does not exceed 5 mW. Or you could measure the first order spots (closest to the 0th order, the reflected/transmitted beam), and make sure THOSE don't exceed 5 mW and then block the main one.

PS: sorry for bringing a thread back from the dead, but I read diffraction and that is one thing I am proud for knowing about, because very few people do.

Thanks very much, alanbrito! At least now I know that the theoretical approach really is impractical. My project has been delayed somewhat, but I will try to go the empirical route. The problem will be to find an eye-save solution that still produces dots with sufficient visibility for daylight conditions.

A different thought I had in the meanwhile is to try to find a mechanical solution in form of some (hopefully) simple contraption that produces a flickering dot matrix by reflecting the source beam, e.g. via rotating mirrors. I hope I will get help from some of the laser show geeks in this forum. But I should open a new thread for this.

Again, thanks to all who replied to my original question!